Telephoto optical design



United States Patent 3,045,548 TELEPHOTO OPTICAL DESIGN James G. Baker,Winchester, Mass., assignor to the United States of America asrepresented by the Secretary of the Air Force Filed Apr. 10, 1959, Ser.No. 805,642 2 Claims. (Cl. 88-57) This invention relates to telephotolenses and more particularly to that type corrected for sphericalaberration, coma, astigmatism, curvature of field, and distortion, aswell as the chromatic aberrations of lateral and longitudinal color, andcertain higher order variations of the above mentioned aberrations,being distinguished by a four component construction, two forward of thestop and two behind the stop. In this construction the rays for infiniteconjugate object plane are always converging through the entire system.In ordinary telephoto lenses this continuous convergence is usually truebut the circumstance leads to distortion of the chief rays except forspecial constructions in the prior art designed to reduce or eleminatethe condition. In the invention claimed herein a novel construction hasbeen found that not only minimizes distortion but also permits aconsiderable reduction of the physical length of the optical systemrelative to the focal length without sacrificing other essentialcharacteristics of performance.

Telephotos of the prior art commonly have a front positive group and arear divergent group with respect to a centrally located stop.Achromatization of the two groups usually leads to strongly curvedsurfaces which in turn either cause unacceptable aberrations or requirethat the 1 number of the telephoto 'be limited. For example, a normaltelephoto lens covering a total field of 15 degrees might have a lensspeed of f/ 5.0 to f/ 8.0, except for those of unusually short focallength, where lens speeds of f/4.5 occasionally have been obtained. Ifthe angular field is increased, the f number as a rule also increases.Thus, a telephoto lens covering a 30-degree field might have a speed ofonly f/ 8, although occasionally one at f/6.3 might be found.

Accordingly, it is an object of the invention to provide an improvedtelephoto lens system which has a successful aspheric lens which can beincorporated in an aerial camera.

Another object of the invention is to provide a telephoto lens systemwhich is substantially corrected for spherical aberration, coma,astigmatism, curvature of field, and distortion as well as the chromaticaberrations of lateral and longitudinal color and certain higher ordervariations of these aberrations.

Still another object of the invention is to provide a telephoto lenssystem which is unusually compact and especially suited for aerialphotographic reconnaissance operations.

Symbols in the field in which this invention occurs are well establishedand Roman numerals I, II, etc. beginning with oncoming light indicatelens elements. Arrows indicate light energy paths. Lens surface radii ofcurvature are indicated by the letter R. Lens radii of curvature arepositive for lens surfaces which are convex to oncoming light and arenegative for lens surfaces which are concave to oncoming light. Theletter 1 indicates the axial thicknesses of lenses. The letter 5indicates the axial air spaces between lens element surfaces. m; is therefractive index for the sodium light D line of the spectrum of lambda5893A. V is the reciprocal dispersive power or Abb number. The lenssystem described herein may be constructed from commercially availableglass types.

The telephoto lens systems described herein is especially suited tomedium to small angular fields but can be designed to have lens speedsof the order of f/4.0 for "ice systems of great focal length to f/ 3.0for those with short focal length. This novel optical system is alsocharacterized by little or no vignetting at the edge of the adoptedfield, a circumstance made possible by the unusflal construction whichproduces a sharp image at the edge of the field. The limiting aberrationis high order astigmatism that sets in very rapidly to limit the field,but which in turn causes no trouble in the quality of the image formedium to small field angles. Oblique spherical aberration has beeneliminated by choice of glass types and cemented surfaces and by themost favorable values of the curvatures and separations. Coma andoblique coma are both quite highly corrected, the residuals in the imageplane for long focal lengths being not larger than a few microns. Inerrors of the aperture the limiting aberration turns out to be chromaticvariations in the oblique spherical and oblique coma, which however, donot reach serious proportions until either the higher order astigmatismhas limited the off-axis angle or until the spectral range is increasedinto the deep violet or deep red.

For a better understanding of the invention reference may be made to theaccompanying drawings in which are shown two telephoto lens systemsaccording to the invention wherein:

FIG. 1 is a form of f/4.0 telephoto lens system cover ing a 12 totalfield;

Table 1 includes the numerical data of the lens system shown in FIG. 1;

FIG. 2 is a form of f/ 5.0 telephoto lens system covering a 10 totalfield; and

Table 2 includes the numerical data of the lens system shown in FIG. 2.

In the drawings the light energy enters the lens system as indicated bythe directional arrows shown. Consecutively numbered subscripts are inthe order of the passage of light energy through the system. The lenselements are indicated by Roman numerals. The lens surface curvaturesare of radii indicated by the letter R, with the radii positive wherethe lens surface is convex to approaching light and with the radiinegative when the lens surface is concave to approaching light. The lensaxial thicknesses are indicated by the letter t and the axial air spacesbetween adjacent lens surfaces are indicated by the letter S. Thesystems includes a stop 10 and a focal plane 11.

Referring now to FIG. 1, a chart of values for the components of thelens system shown therein follows: Optical design of a form of f/4.0telephoto for a 12 total field in terms of the focal length taken asunity.

[f= 1.000, mean color 5461, spectral coverage 4341 to 6900 approx] Thestop lies 0.029 from the vertex of R In the above chart, conversion toinches for a f=24 lens is accomplished by multiplying R values by 24(focal length) as for example R O.4822 24=l1.57 inches, R 0.1973 24=4.74inches, etc.

In the lens system shown in FIG. 1, for a focal length of 24 inches, thestop lies 0.702 inch from R and has a clear aperture of 2.622 inches atf/ 4.0.

FIG. 2 shows a lens system having the following chart of values ofcomponents: Optical design of a form of f/ 5.0 telephoto for a 10 totalfield in terms of the focal length taken as unity.

[f=1,000 inches, mean color 5461, spectral coverage 4341 to 6900;refocus for yellow or red filter] Lens 111) V Radii Thlcknesses RI=0.3307 I 1. 613 58.6 h =0.03l2

R1 -plano S =0.00l3 Rs =0.l556 II 1. 613 58. 6 lz=0.0477

R =p1ano III 1. 617 36. 6 tz=0.0220

Rs =0.07279 IV 1.613 58. 6 t =0.0480

S2=0.0211 R: =1.905 1. 596 39. 2 ts==0.0l66 Ra =0.1010 1. 592 58. 2ts=0.0030

R9 =0.0G56 1. 622 53. 1 i1=0.0225

Ss=0.4880 Ru=0.3453 l. 613 58. 6 la=0.0475 Ru=-O.3847

BF=0.030O

The stop is formed by the adopted clear aperture of R The optical systemaccording to the invention comprises as its first component a collectivemember I, which preferably is a simple element.

The second component of the system, consists of three elements. Thiscomponent is of meniscus form and, neglecting the great thickness, is ofnegative effect in the system. One can describe this thick component asbeing a negative meniscus component whose air surface on the longconjugate side is convex and whose air surface on the short conjugateside, adjacent to the stop, is strongly concave. The color correction ofthe system requires that at least two elements be used. For fastersystems and those of unusually critical correction, three or moreelements are employed to prevent chromatic errors in the lower rim rays.One can also vignette these rays in the simpler system, but with threeor more elements, adequate correction can be found with little or novignetting. Also, the component as a rule is so thick that there is nodifficulty in adding elements for the purpose of special corrections.

A diaphragm stop 10 is interposed between the second and thirdcomponents.

The third component of the system follows the stop 10 and consists ofthree elements. Its function is primarily to spread out some of thenegative telephoto power that otherwise might be added to the surfaceimmediately preceding the stop on the long conjugate side, which wouldin that event render almost hopeless any attempt to control theaberrations. Another of its functions is to have added negative power toproduce an enhanced telephoto effect without serious increase inaberrations, the offsetting positive power being added to the fourthcomponent described below. In addition this third component helps effectcorrection of the lateral and longitudina lcolor, while at the same timea judicious choice of the glass types and associated cemented surfaceswill control oblique coma and oblique spherical aberration.

This third component lies so low in relative height that its diameterremains small. Hence, further compounding of this component isrelatively inexpensive and yet marked improvement in the system canthereby be obtained. For example, one or both of the air surfaces may bemade aspheric or the aspheric or aspherics may be replaced with one ormore cemented surfaces within the concept of this invention. When strongcemented surfaces are used to control the oblique correction of theupper rays, care must be taken in the choice of the V-value of the glasstypes on either side of the strong refraction. The addition may be madeof another element with weaker curves to effect color correction withoutat the same time adding chromatic angular displacements of the obliquerays.

The fourth component lies in the neighborhood of the focal surface. Itis of positive power and of bi-convex form insofar as its air surfacesare concerned and functions to produce a small or zero Petzval sum forthe overall system, without at the same time destroying the telephotoeffect already achieved in the first three components described above.The shape and location of this component also help correct astigmatismand distortion, and lateral color. From another point of view the fourthcomponent comes into existence by the addition of extra negative powerto the second and third components, which negative power enhances thetelephoto effect, which negative power is thus off-set by the positivepower of the fourth component. The location of the fourth component thenserves mostly to flatten the field. The bending serves to reducedistortion and to eliminate astigmatism.

It is desirable to have at least one aspheric surface in the system.While in general it would be desirable to have the aspheric correctiondistributed in a certain way between the two air surfaces adjacent tothe stop on either side of the stop, practicality requires at least onesolution where the aspheric is on one or the other of these twosurfaces. In FIG. 1 showing a form of f/4.0 telephoto, the asphericcorrection is on the surface immediately following the stop, lying thenon the short conjugate side of the stop. However, further calculationsat hand demonstrate the effectiveness of having the aspheric correctionput instead onto the surface immediately preceding the stop, as in FIG.2, being then on the second component. As mentioned, a still bettersolution would be to have the correction split between the two, butgreater expense of construction is thereby incurred.

Still other aspherics can be used to advantage within the concept ofthis invention. In the system shown in FIG. 1 it has proved desirable tohave an aspheric correction added to the back side of the firstcomponent, this correction being of turned-down nature to off-set thecemented surface in the second component. In still another form, anaspheric can be profitably added to the rear air surface of the thirdcomponent, either to improve other corrections or to serve to eliminateone or more elements otherwise required in the third component forcorrection of the upper oblique rays.

The rear surface of the fourth component which is then adjacent to thefocal plane 11 effects correction for distortion, which comes about fromthe refraction of the chief rays. This refraction is accompanied byspherical aberration of the chief rays, which therefore is a distortionof higher order. The fifth order distortion is therefore of barrelnature, and the off-setting third order distortion is of pincushionnature. The two can be brought exactly into balance at a designatedfield angle. The inner and outer residuals thereafter depend on theadopted field angle and the focal length, if measured in lineardisplacement on the focal plane. It is obvious that an aspheric surfaceor surfaces on the fourth component can be employed to eliminate eventhe higher order distortions, if necessary, or more important, toimprove the correction for higher order astigmatism and thereby toextend the usable field. Higher order chromatic variation of the chiefray refraction can also be troublesome. The elimination of thisaberration depends on zonal achromatization of the fourth componentwhich may be a flint and crown doublet, cemented together, if desired.

The system as a whole must be designed for color balance over the fieldand aperture. Both may be achieved to the highest state of correctioncomponents, and by the use of aspheric by the adoption of propersurfaces as disclosed herein. Systems so designed provide speeds as fastas f/ 3 for field angles of about 15 degrees with satisfactoryperformances from violet to deep red, in spite of the asymmetry ofconstruction and telephoto effect.

The telephotos disclosed herein have a strong secondary spectrum whichmay be minimized at any assigned wave length. The rays for colors oneither side of the adopted mean color in the system focus longer andlonger the farther removed the color is from the mean. This secondaryspectrum exists both in the longitudinal and in the lateral color.

Calculations show that the longitudinal state of correction is verynearly constant over the field, at least in the skew or obliquedirection. The tangential performance shows sensitivity to chromaticcoma for those combinations which have unfavorable dispersions atcemented surfaces. On the other hand, the lateral color varies over thefield; that is, thewave length of maximum distance of the chief ray fromthe center of the field varies with the field angle.

In the inner field the mean wave length is in the violet. In theoutermost field the mean wave length has moved into the red. At a chosenfield angle, such as 87% of the maximum off-axis field angle, the meanwave length lies in the blue-green, for a system balanced for thiscolor. The rate of variation depends largely on the construction of thefourth component VI. In the simpler systems the fourth component mayconsist of only one element. If this element VIII in FIGS. 1 and 2 ismade of dense flint glass to reduce the curvatures elsewhere in thesystem, there is marked variation of chief ray refraction with colorover the field. If the fourth element is made of barium crown glass, andother chromatic curves are modified, the residuals from the lateralcolor variation become reduced.

The first component I may be achromatized, as being made of two or moreelements of crown and flint glass corrected for chromatic aberration, ifpreferred, for reducing the difficulties of achromatizing the lateralcolor. A cemented doublet of crown and flint glass (not shown), also mayreplace the fourth component for the reduction and the elimination ofthe higher order tendency toward undercorrected astigmatism. An 5aspheric term on the last surface of the fourth component eliminatesthis astigmatism. A steep cemented curve turned away from the stop inone type and turned toward the stop 10 in the preferred form of doublet,with'a slight index difference in the sense of the positive clementlower than the adjacent negative element index, are within the conceptof this invention. Choice of dispersions completely eliminate thechromatic spherical aberration of the chief rays caused by the rearsurface chromatic refraction to negligible residuals. With the rearcomponent fully achromatized, the lateral color is reduced to a stablesecondary spectrum effect where the mean wave length remains about fixedin the spectrum as the field angle varies. The amplitude of thesecondary spectrum increases with the field angle.

In the lens system shown in FIG. 1 for a 24 inch focal length, the stop10 lies 0.702 inches from the lens surface R and has a clear aperture of2.622 inches at f/4.0. The lens surface R is an aspheric surface with aturnedup edge. The clear aperture of the lens IV surface R is formed bya fiat seating ledge. The actually used clear aperture is 2.823 inchesbut the excess is needed for the purpose of obtaining a smooth asphericcurve. The surface R is rather strongly aspheric but the requirementsfor precision on depth are of the order of 0.001 inches. S-moothness isnecessary.

The monochromatic performance of the optical system illustrated in FIG.1 by ray calculation is excellent. The on-axis image is well within theRayleigh limit for the designated apherics on IBM sheets. The tangentialand the skew images at 0.06, 0.09 and 0.104 radians off-axis are wellwithin the Rayleigh limit, except for a minor percentage of the light.The images out to 0.09 radians off-axis are practically unvignetted, andeven at the edge of the field or 0.104 radians off-axis, theillumination is of the order of The aspheric rear surface on the fieldflattening surface R is aspheric in order to obtain a flat, anastigmaticform. Calculations at 0.06, 0.09 and at 0.104 radians off-axis show aflat tangential image within a few hundredths of a millimeter of thesame common focal plane as for the on-axis image.

With respect to the minimum of the secondary spectrum color curve, thecolor correction lies in the blue-green. The longitudinal color isfarily stable over the field. There is some primary color which isintroduced to balance the overcorrected chromatic spherical aberration,producing the mean correction at the 0.7 zone.

The lateral color correction lies in the blue-green for the 87% fieldangle. In the intermediate field, the best lateral color correction liesin the violet. The residual lateral color curve is of secondary spectrumnature. The variation with field angle is actually due to chromaticdistortion as balanced by primary lateral color.

The correction for longitudinal and lateral color are optimum for theconstruction. The monochromatic skew performance is uniformly excellentover the entire field. In the outermost field the extreme rim rays inthe skew direction exceed the Rayleigh limit, but the percentage oflight that is so lost is very small. Other hybrid chromatic deficienciesin the optical system are of inconsequential magnitude. The asphericsurface R of FIG. 1 is highly precise and smooth in order that thedesign may achieve critical performance. The turned-up edge of R isquite far from a spherical surface at f/4.0. In this instance even theepsilon term contributes significantly.

Now referring to the lens system shown in FIG. 2, the lens surface R isan aspheric surface with a turned-up edge. For a 24 inch focal length,values are beta 2.4873; gamma 23.25; delta 6707; and epsilon 0.000,where the Greek letters represent the successive coefficients ofpolynomial terms describing the aspheric correction, starting with the4th degree term.

The stop 10 following the lens surface R is formed by the cell lip onthe surface R This stop serves to restrict the clear aperture of theaspheric surface R The surface R preferably is made slightly aspheric toflatten the field precisely. Otherwise, use of a purely sphericalsurface leaves the intermediate field slightly overcorrected and theoutermost field slightly undercorrected.

In general the performance of the optical system in FIG. 2 is comparableto that of the f/4.0 version of the invention. A similarly operative 36inch f/ 6.7 is within the conception of this invention. The reduction infield compared with the device shown in FIG. 1 permits a version of theinvention that is improved for lateral color. The longitudinal color issubstantially stable over the field. The aspheric lens surface R iscombined with a differential aspheric correction to eliminate distortionfor a mean field angle, with very small residuals elsewhere. Themonochromatic skew performance of the optical system in FIG. 2 isuniformly excellent over the entire field. The aspheric surface on theFIG. 2 lens surface R is highly precise and smooth for the object ofachieving critical performance. The turned-up edge is quite far from aspherical surface at f/ 5.0. The aspheric surface preferably is figuredby knife-edge for best results, once other means have brought thesurface within figuring distance of the specified mathematical curve.

It is obvious that the focal lengths of the telephoto lens systemsdescribed herein may be scaled to larger and to smaller focal lengthswith little or no revision. The

optical performance of the shorter focal lengths is even better than theoptical performance of the longer focal length. For focal lengths of 6to 8 inches, the field covered is comparable to that of miniaturephotography, to which this telephoto construction is readily adapted.The image quality conforms fully to all that is expected of a lens forminiature cameras, and hence fills a need for the telephoto attachmentto such cameras in the 6 to 12 inch focal length range at speeds fromf/3.0 to f/5.0. Other telephoto lenses of simple design serve thereafterfor still greater focal lengths.

Having thus described my invention, what I claim as new and desire tosecure by Letters Patent of the United States is:

1. The telephoto lens system comprising a plurality of axially alignedcomponents having numerical data substantially as follows:

[Focal length 1:1.000]

Lens m: V Badil Thicknesses R1 =0.4822 I 1. 613 58.6 t1=0. 0369 R1=plauo 8 :0. 0031 R; =0. 1973 II 1.613 58.6 lz=0.063l

R4 =plano III 1.617 36.6 13:0. 0391 R5 =0. 0904 IV 1.613 58.6 t4=0. 0833S1=0. 0376 R1 =2. 659 V 1.617 36.6 =0. 0198 v R; =0. 1227 VI 1.607 59.5ta=0.0042

R9 =0. 06704 VII 1.620 60.3 l7=0. 0370 S;=0. 3532 R11=0.41B8 VIII 1.61358.6 ta=0. 0632 Rip-0.3300

in which n is the index of refraction for the D line of the spectrum, Vis the Abb number, R R .indicate the radii of the individual surfacesstarting from the front, 1 t indicate the actual thicknesses of theindividual elements, and S S indicate the axial lengths of the airspaces between the components, BF being the back focal distance.

2. A telephoto lens system comprising a plurality of axially alignedcomponents having numerical data substantially as follows:

[Focal length I: 1.000]

Lens no V Radii Thickncsses R =0. 3307 I 1. 613 58. 6 t1=0. 0312 R:=plano S =0. 0013 R: =0. 1556 II 1. 613 58. 6 l2=0. 0477 R =plano III 1.617 36. 6 l =0. 0220 Rs =0. 07279 IV 1. 613 58. 6 =0. 0480 Sz=0. 0211R7 1. 905 1.506 39. 2 is=0. 0166 Rs 0. 1010 1. 592 58. 2 ts=0. 0030 Re=0. 0656 1. 622 53. 1 i7=0. 0225 Sa=0. 4880 R11=0. 3453 1. 013 58. 6ta=0. 0475 Riz= 0. 3847 in which n is the index of refraction for the Dline of the spectrum, V is the Abb number, R R indicate the radii of theindividual surfaces starting from the front, t t indicate the actualthicknesses of the individual elements, and S S indicate the axiallengths of the air spaces betwen the components, BF being the back focaldistance.

References Cited in the file of this patent UNITED STATES PATENTS2,171,274 Merte Aug. 29, 1939 2,452,909 Cox Nov. 2, 1948 2,600,805 ReissJune 17, 1952 2,629,285 Baker Feb. 24, 1953 2,645,973 Ito July 21, 19532,685,230 Baker Aug. 3, 1954 2,715,855 Altman Aug. 23, 1955 2,821,113Baker Jan. 28, 1958 2,862,418 Lowenthal Dec. 2, 1958 FOREIGN PATENTS763,502 Great Britain Dec. 12, 1956

